What is the directrix x^2-2x-3 ?

The directrix x^2-2x-3 is y=-17/4

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directrix x^2-2x-3

directrix

x^{2} - 2 x - 3

y = - \frac{17}{4}

Solution steps

Rewrite

y = x^{2} - 2 x - 3

in the standard form

4 \cdot \frac{1}{4} (y - (- 4)) = (x - 1)^{2}

(h, k) = (1, - 4), p = \frac{1}{4}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(1, - 4)

y-coordinate

y = - 4 - p

y = - 4 - \frac{1}{4}

Refine

y = - \frac{17}{4}

y = (3 x - 7)^{2}

(y + 2)^{2} = - 4 (x - 3)

5 x^{2} - 15 x + 3

x^{2} + 10 x - 24

x (4 - x)